Patchy Colloids, Proteins and Network Forming Liquids:

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Patchy Colloids, Proteins and Network Forming
Liquids Analogies and new insights from
computer simulations Lyon - CECAM - June 26-28
Francesco Sciortino
Dynamics in patchy colloids and network forming
liquids gels and strong glass-forming liquids
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Motivations

• The fate of the liquid state. Gels and phase
  separation essential features (Sticky colloids
  - Proteins, network-forming liquids)
• Models of patchy particles. Why to revisit
  them ?
• Thermodynamic and dynamic behavior of new patchy
  colloids .
• Clues in understanding dynamics in network
  forming liquids (Silica, water.)
• Essential ingredients of strong behavior (A.
  Angell scheme) in glass-forming liquids.

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BMLJ
Liquid-Gas Spinodal
Glass line (D-gt0)
Binary Mixture LJ particles Equilibrium
homogeoues arrested states only for large
packing fraction
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The general (spherical) case(for hard core
complemented by attraction)
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Nmax4 phase diagram - Isodiffusivity lines
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The PMW model
J. Kolafa and I. Nezbeda, Mol. Phys. 161 87 (1987)
V(r
)
Hard-Sphere 4 sites (2H, 2LP) Tetrahedral
arrangement H-LP interact via a SW Potential,
of range l0.15 s.
r
u0
(energy scale)
s
(length scale)
Bonding is properly defined --- Lowest energy
state is well defined
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The PMS ModelFord, Auerbach, Monson,
J.Chem.Phys, 8415,121 (2004)
Silicon Four sites (tetrahedral)
SW interaction between Si sites and O sites
Oxygen Two sites 145.8 o
sOO1.6 s l1-3 /2s
1/2
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Equilibrium phase diagram (PMW)
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Pagan-Gunton
Pagan and Gunton JCP (2005)
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Equilibrium Phase Diagram PSM
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Critical Point of PMW
GC simulation BOX SIZE6s TC0.1095 fC0.153
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Critical point PSM
Critical Point of PMS
GC simulation BOX SIZE9s TC0.075 fC0.0445
s0.45
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Potential Energy for the PMW
Optimal density !
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PMW energy
Potential Energy -- Approaching the ground state
Progressive increase in packing prevents
approach to the GS
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E-Egs vs. 1/T
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Potential Energy along isotherms
Optimal density Hints of a LL CP
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S(q) in the phase-separation region
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S(q) in the network region
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PMS -Potential Energy
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PMS E vs 1/T
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PMSStructure (r-space)
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Structure (q-space)
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E vs n
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Summary of static data
Phase Separation Region
Packing Region
Optimal Network Region - Arrhenius Approach
to Ground State
Region of phase separation
Packing Region
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R2 vs t
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Diffusion Coefficient
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D along isotherms
Diffusion Anomalies
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Isodiffusivities .
Isodiffusivities (PMW) .
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Si dynamic in PSM
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Comparing different potentials
Bonded-triples angle
q
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How to compare these (and other) models for
tetra-coordinated liquids ? Focus ONLY on the
of 4-coordinated particles (other particles are
bond-mediators) () Length scale ----
nn-distance among 4-coordinated particles
(l44) Scaled Density (l44 )3/V Energy scale
---- Tc
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Comparing E(n) at low T
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Comparing isodiffusivity lines
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Analogies with other network-forming potentials
ST2 (Poole)
SPC/E
Slower on compression
Faster on compression
BKS silica (Saika-Voivod)
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Water Phase Diagram
F 0.34
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Comments

• Directional interaction and limited valency are
  essential ingredients for offering a new final
  fate to the liquid state and in particular to
  arrested states at low f
• The resulting low T liquid state is (along
  isochores) a strong liquid. Directional bonding
  is essential for being strong.
• Gels and strong liquids are two faces of the same
  medal.

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Graphic SummaryTwo glass lines ?
Fragile Liquids - Colloidal Glasses
Strong liquids - Gels Arrest line
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Coworkers
Cristiano De Michele (PMW,PMS) Simone Gabrielli
(PMW) Piero Tartaglia Emanuela Zaccarelli
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http//www.socobim.de/
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Gelation as a result of phase separation
(interrupted by the glass transition)
T
T
f
f
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Density anomalies
Density Anomalies (and possible 2nd CP)
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D vs (1-pb)
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D vs (1-pb) --- (MC)
D f04 (Stanley-Teixeira)
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Foffi aging
G. Foffi, E. Zaccarelli, S. V. Buldyrev, F.
Sciortino, P. Tartaglia Aging in short range
attractive colloids A numerical study J. Chem.
Phys. 120, 1824, 2004